Chemical Engineering Research & Design, Vol.82, No.9, 1117-1136, 2004
Mixing effects in silver halide precipitation - Linking theory with practice using a multi-mechanism model
This paper presents a fully mechanistic model of silver halide precipitation that couples the mixing field and mixing rates with instantaneous nucleation, size-dependent growth, full thermodynamic equilibria and crystal population balances. The mixing model uses an Eulerian frame of reference to define the mixing field in the bulk of the kettle, and a Lagrangian frame of reference to model the feed plume. The feed is divided into differential feed volumes which move through the kettle and are mixed with the bulk at rates defined by the Eulerian model of the mixing field. This model framework allows a coupling between the mixing field and the precipitation mechanisms at every time step and every location in the kettle. The model results agree closely with experiments over two orders of magnitude in molar feed rate and a factor of 4 change in feed concentration, with no fitting parameters required. The model is used to probe the precipitation process, showing that the effect of mixing on precipitation is complete at the end of the dissolution period. Simulations of surface and impeller feeds are compared with the ideally mixed limit, and a new mixing limit is identified: the convective stoichiometric limit. Where a high feed concentration or a high feed rate is required, the molar feed rate of the fed reagent may exceed the amount of the second reagent which IS vailable by mixing from the local convective flow. At the convective stoichiometric limit, the reaction in the feed plume is stoichiometrically limited by the surrounding convective flow. As a concluding step, all of the mixing effects are illustrated in a comparison of two possible scale-up protocols and their effect on the precipitation results.